Three humans, three monkeys, and a boat problem
February 11th, 2013 at 4:37:50 PM
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On one shore of the river are three humans, two small monkeys, one big monkey, and a boat. The capacity of the boat for any mix of two humans/monkeys is two. Only the humans and large monkey are strong enough to row the boat.
If at anytime, on either shore, the monkeys outnumber of the humans, they will eat them. The goal is to get everybody to other shore safely. How do you do it?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 11th, 2013 at 4:43:38 PM
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Quote: WizardOn one shore of the river are three humans, two small monkeys, one big monkey, and a boat. The capacity of the boat for any mix of two humans/monkeys is two. Only the humans and large monkey are strong enough to row the boat.
If at anytime, on either shore, the monkeys outnumber of the humans, they will eat them. The goal is to get everybody to other shore safely. How do you do it?
#Humans = #Monkeys (of any size) = Safe?
#Humans<#Monkeys (while on the boat) = Eaten?
Edit: Is an unattended monkey of any size okay?
Simplicity is the ultimate sophistication - Leonardo da Vinci
February 11th, 2013 at 5:03:19 PM
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Death check: if there are two monkeys on the shore, and two humans in the boat, can those turn into human+monkey on shore and human+monkey in the boat without one of the humans getting eaten?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
February 11th, 2013 at 5:08:00 PM
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I get 11 trips (checking my answer via the internet)
Assuming the big monkey can drive the boat unattended, and that the monkeys will not wander off if unattended by humans.
b=boat
M=big monkey
m=little monkey
H=big human
h=little human
From Way To
bMmmHhh
Mmhh > bHm
bMmHhh < m
Hhh > bMmm
bMHhh < mm
Mh > bHhmm
bMmHh < hm
mm > bHhhM
bMmm < Hhh
m > bHhhMm
bMm < Hhhm
> bMmmHhh
Assuming the big monkey can drive the boat unattended, and that the monkeys will not wander off if unattended by humans.
b=boat
M=big monkey
m=little monkey
H=big human
h=little human
From Way To
bMmmHhh
Mmhh > bHm
bMmHhh < m
Hhh > bMmm
bMHhh < mm
Mh > bHhmm
bMmHh < hm
mm > bHhhM
bMmm < Hhh
m > bHhhMm
bMm < Hhhm
> bMmmHhh
Simplicity is the ultimate sophistication - Leonardo da Vinci
February 11th, 2013 at 5:20:58 PM
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#Humans = #Monkeys (of any size) = Safe? Yes
#Humans<#Monkeys (while on the boat) = Eaten? Not possible. Max two on the boat.
Edit: Is an unattended monkey of any size okay? Yes
Like the two monkeys pulling a human out of the boat and eating him on the shore? No, that can't happen. The two humans in the boat would beat the two monkeys back.
Aye, there are no big and little humans. Just three total, size does not matter with the humans.
#Humans<#Monkeys (while on the boat) = Eaten? Not possible. Max two on the boat.
Edit: Is an unattended monkey of any size okay? Yes
Quote: MathExtremistDeath check: if there are two monkeys on the shore, and two humans in the boat, can those turn into human+monkey on shore and human+monkey in the boat without one of the humans getting eaten?
Like the two monkeys pulling a human out of the boat and eating him on the shore? No, that can't happen. The two humans in the boat would beat the two monkeys back.
Aye, there are no big and little humans. Just three total, size does not matter with the humans.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 11th, 2013 at 6:04:25 PM
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Put monkey A in the boat and one human A. Drop the monkey A off first. Human A rows back to the start location and picks up monkey B. They row to the drop location and human A jumps out. Monkey B stays in the boat and rows back to the start location and picks up the human C. Human C gets dropped off at the new location. Monkey B rows back to pick up the final monkey.
If size matters, drop off a smaller monkey first. And pick up a big monkey second.
If size matters, drop off a smaller monkey first. And pick up a big monkey second.
February 11th, 2013 at 6:08:45 PM
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February 11th, 2013 at 6:30:53 PM
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Quote: AsswhoopermcdaddyPut monkey A in the boat and one human A. Drop the monkey A off first. Human A rows back to the start location and picks up monkey B. They row to the drop location and human A jumps out...
At that moment the opposite shore would have 2 monkeys and one human, and the monkeys would eat the human. In future submissions please use spoiler tags and note whether you are referring to the small or large monkeys.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 11th, 2013 at 8:10:51 PM
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Quote: Wizard... Just three total, size does not matter with the humans.
I think there is a large female population that would take exception to that statement, taken out of context, of course.
Always borrow money from a pessimist; They don't expect to get paid back !
Be yourself and speak your thoughts. Those who matter won't mind, and those that mind, don't matter!
February 11th, 2013 at 8:12:30 PM
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I remember a much simpler version of this. You, a dog, a chicken, and a bag of grain.
Unattended dog and chicken will result in dead chicken.
Unattended chicken and grain will result in no grain.
Neither the dog nor chicken will run away if left alone.
And it's a very small boat with room for you and one of those items.
Not hard to figure a solution when you can trust the dog alone with the grain.
Unattended dog and chicken will result in dead chicken.
Unattended chicken and grain will result in no grain.
Neither the dog nor chicken will run away if left alone.
And it's a very small boat with room for you and one of those items.
Not hard to figure a solution when you can trust the dog alone with the grain.
February 11th, 2013 at 8:18:57 PM
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Quote: zarg7883I remember a much simpler version of this...
Homer Simpson struggles with this puzzle in one episode; I don't recall which.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 11th, 2013 at 8:22:31 PM
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Quote: zarg7883I remember a much simpler version of this. You, a dog, a chicken, and a bag of grain.
Unattended dog and chicken will result in dead chicken.
Unattended chicken and grain will result in no grain.
Neither the dog nor chicken will run away if left alone.
And it's a very small boat with room for you and one of those items.
Not hard to figure a solution when you can trust the dog alone with the grain.
xkcd: Logic Boat
“Man Babes” #AxelFabulous
February 11th, 2013 at 9:13:04 PM
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Quote: sodawaterhttp://www.youtube.com/watch?feature=player_detailpage&v=8gciFoEbOA8#t=16s
I love this reply. :)
"Although men flatter themselves with their great actions, they are not so often the result of a great design as of chance." - Francois De La Rochefoucauld
February 11th, 2013 at 9:20:41 PM
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Let's not get too off topic. I'm still looking for a smartypants to get the right answer.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 11th, 2013 at 9:53:00 PM
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There's no law stating that the monkey can't navigate the boat. We just make the assumption that he's too stupid. I don't make that assumption.
Let the trip be from shore 1 to shore 2.
Trip one: big monkey / little monkey, drops off little monkey. on shore 1: three humans and one monkey; on shore 2: one monkey. Big monkey driving the boat.
Trip two: big monkey / human, drops off human. On shore 1: two humans and one monkey; on shore 2: one monkey and one human. Big monkey still drives.
Trip three: big monkey / human, drops off human. On shore 1: one human and one monkey; on shore 2: one monkey and two humans. Big monkey is driving.
Trip four: big monkey / human, drops off big monkey. On shore 1: one monkey; on shore 2: two monkeys and two humans. Human drives.
Trip five: Human / small monkey, both dropped off. Everyone's happy.
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You want the truth! You can't handle the truth!
February 11th, 2013 at 10:10:08 PM
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BM, after the return of trip 3 there will be too monkeys and one human on the shore of origin, and we don't want that.
You are correct that the big monkey may navigate the boat by himself.
The smartypants award is still up for grabs.
You are correct that the big monkey may navigate the boat by himself.
The smartypants award is still up for grabs.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 11th, 2013 at 10:15:59 PM
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I don't think so. The big monkey stays on the boat.
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You want the truth! You can't handle the truth!
February 12th, 2013 at 12:19:51 AM
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H = human
M = big monkey
m = small monkey
| Shore 1 | Boat | Shore 2 |
|---|---|---|
| HHHMmm | ||
| HHMm | Hm> | |
| HHMm | <H | m |
| HHH | Mm> | m |
| HHH | <M | mm |
| HM | HH> | mm |
| HM | <Hm | Hm |
| Hm | HM> | Hm |
| Hm | <Hm | HM |
| mm | HH> | HM |
| mm | <M | HHH |
| m | Mm> | HHH |
| m | <M | HHHm |
| Mm> | HHHm | |
| HHHMmm |
February 12th, 2013 at 1:42:33 AM
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Quote: boymimboI don't think so. The big monkey stays on the boat.
He would see that if he gets out he can gang up with the other monkey and eat the human. They monkeys' priorities are bloodthirsty first, achieving the goal second.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 12th, 2013 at 1:46:56 AM
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Quote: stargazer
H = human
M = big monkey
m = small monkey
Shore 1 Boat Shore 2 HHHMmm HHMm Hm> HHMm <H m HHH Mm> m HHH <M mm HM HH> mm HM <Hm Hm Hm HM> Hm Hm <Hm HM mm HH> HM mm <M HHH m Mm> HHH m <M HHHm Mm> HHHm HHHMmm
Correct! Congratulations, you are the smarty pants of the day.
My own opening was different but after the first four steps our solutions are the same. I'm pretty sure there may be other equally short solutions, but nothing shorter.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 12th, 2013 at 7:46:16 AM
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Quote: WizardAt that moment the opposite shore would have 2 monkeys and one human, and the monkeys would eat the human. In future submissions please use spoiler tags and note whether you are referring to the small or large monkeys.
Hi Wizard,
By my post, this is what I meant visually. If the monkey stays in the boat, they won't cannibalize each other on shore.
Shore A.......Boat............Shore B
MmmHHH...mH >
MmHH..........H...............m
MmHH.........< H............m
MmHH..........H...............m
mHH...........HM >...........m
mHH............M...............Hm
mHH...........< M.............Hm
mHH.............M..............Hm
mHH............HM >..........Hm
mH................M.............HHm
mH...............< M...........HHm
mH.................M............HHm
m................HM >..........HHm
m..................M.............HHHm
m..............< M..............HHHm
m.................M..............HHHm
...................Mm >.........HHHm
....................................HHHMmm
February 12th, 2013 at 7:23:58 PM
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Quote: AsswhoopermcdaddyIf the monkey stays in the boat, they won't cannibalize each other on shore.
They will. The monkey's priorities are to kill the humans first and achieve the goal second. They would have no compunction to leap out of the boat to eat the humans if it would put them in the majority.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
